Multifocal ophthalmic lens

ABSTRACT

A method of designing a multifocal ophthalmic lens with one base focus and at least one additional focus, capable of reducing aberrations of the eye for at least one of the foci after its implantation, comprising the steps of: (i) characterizing at least one corneal surface as a mathematical model; (ii) calculating the resulting aberrations of said corneal surface(s) by employing said mathematical model; (iii) modelling the multifocal ophthalmic lens such that a wavefront arriving from an optical system comprising said lens and said at least one corneal surface obtains reduced aberrations for at least one of the foci. There is also disclosed a method of selecting a multifocal intraocular lens, a method of designing a multifocal ophthalmic lens based on corneal data from a group of patients, and a multifocal ophthalmic lens.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to a multifocal ophthalmic lens, and morein detail to a multifocal intraocular lens with reduced aberrations.

TECHNICAL BACKGROUND

Generally, a multifocal lens is required to provide a certain power forfar vision and different, usually greater (more positive), powers formid and near vision, the additional power for mid and near visionsometimes being referred to as “mid-add” and “near-add”, which isusually expressed in dioptres. Multifocal lenses with two foci arereferred to as bifocal.

Compared with monofocal ophthalmic lenses, multifocal ophthalmic lensesoffer the advantage of reduced spectacle dependency, whereas patientswith monofocal lenses generally need reading spectacles. In an idealsituation, the patient will have good vision in distance and near, whilethe depth of focus will enable vision in the intermediate. In thissituation, the patient doesn't need spectacles in any situation.However, since a multifocal lens splits the available light into two ormore foci, the visual quality in each focus is somewhat reduced. When adistant object is focused on the retina, a blurred image is superimposeddue to the presence of the additional foci and vice versa, whichobviously reduces the image quality. The reduced visual quality can bedivided in reduced contrast sensitivity and appearance of opticalphenomena, like straylight and halos. Moreover a patient has to undergoa learning period after implantation, as the two (or more) simultaneousimages displayed on the retina can be confusing in the beginning. Inmost cases, the blurred image is discarded by the human visualperception and retinal processing system.

Usually, multifocal lenses are designed according to one or more of thefollowing optical principles:

-   -   1. Diffractive type: conventional refractive lens combined with        diffractive optics that splits light into two or more focal        points.    -   2. Refractive optics with annular zones/rings with different        radii of curvatures.

Examples of bifocal and multifocal intraocular lenses are disclosed inU.S. Pat. No. 4,642,112 and U.S. Pat. No. 5,089.024. Examples ofcommercially available multifocal lenses are: model CeeOn® model 811 E,Pharmacia, Kalamazoo, Mich. and SA 40, AMO, Irvine, Calif. The former isbased on diffractive optics, whereby light is partitioned into two focalpoints, one for distance vision and one for near vision. The latter is adistance-dominant, zonal-progressive, multifocal optic with a3.5-diopter near-add.

After IOL implantation, any remaining defocus (sphere) and astigmatism(cylinder) can be corrected by spectacles or contact lenses. Besidefirst order defocus and astigmatism of the eye a number of other visiondefects could be present. For example aberrations of different ordersoccur when a wavefront passes a refracting surface. The wavefront itselfbecomes aspheric when it passes an optical surface that hasimperfections, and vision defects occur when an aspheric wavefront fallson the retina. Both the cornea and the lens in the capsular bagcontribute thus to these types of vision defects if they deviate frombeing perfect or perfectly compensating optical elements. The termaspheric will in this text include both asphericity and asymmetry. Anaspheric surface could be either a rotationally symmetric or arotationally asymmetric surface and/or an irregular surface, i.e. allsurfaces not being spherical.

Recently, in studies on older subjects, it has been discovered that thevisual quality of eyes having an implanted monofocal IOL, havingspherical lens surfaces (hereafter referred to as a conventionalintraocular lens (CIOL)) is comparable with normal eyes in a populationof the same age. Consequently, a 70 year old cataract: patient can onlyexpect to obtain the visual quality of a non-cataracteous person of thesame age after surgical implantation of an intraocular lens, althoughsuch lenses objectively have been regarded as optically superior to thenatural crystalline lens. This result is explained by the fact thatCIOLs are not adapted to, compensate for defects of the optical systemof the human eye, namely optical aberrations.

In order to improve the performance of implanted intraocular lenses,efforts have been made to provide intraocular lenses for implantationthat at least partly compensates for such aberrations (ReducedAberration IOL, or RAIOL). The applicant's own application WO 01/89424discloses an ophthalmic lens providing the eye with reduced aberrations,and a method of obtaining such. The method comprises the steps ofcharacterizing at least one cortical surface as a mathematical model,calculating the resulting aberrations of said corneal surface(s) byemploying said mathematical model, selecting the optical power of theintraocular lens. From this information, an ophthalmic lens is modeledso a wavefront arriving from an optical system comprising said lens andcorneal model obtains reduced aberrations in the eye. The ophthalmiclenses as obtained by the methods are thus capable of reducingaberrations of the eye.

Of current multifocal lenses, the optical quality is lower than forcurrent monofocal lenses. This shows in contrast sensitivitymeasurements on pseudophakic patients. As the visual quality ofmultifocal lenses is relatively low, even minor improvements in opticalquality will lead to visible improvements.

Both WO 00/76426 and U.S. Pat. No. 6,457,826 mentions the possibility tomake an aspheric BIOL. WO 00/76426 does not disclose use of any specificaspheric characteristic in the lens, but just mentions the possibilityto combine an asphere with a diffractive pattern. However, U.S. Pat. No.6,457,826 states that optical corrections can be made by aspherizing anIOL surface, but it is not at all described how this could be done.

In view of the foregoing, it is therefore apparent that there is a needfor multifocal ophthalmic lenses that are better adapted to compensatethe aberrations caused by the individual surfaces of the eye, such asthe corneal surfaces, and capable of better correcting aberrations otherthan defocus and astigmatism, as is provided with conventionalmultifocal intraocular lenses.

SUMMARY OF THE INVENTION

The object of the invention is to provide a multifocal intraocular lensand a method of designing for designing such, which overcome thedrawbacks of the prior art devices and methods. This is achieved by themethod as defined in claims 1, 40 and 81, and by the multifocalophthalmic lens as defined in claims 102, 103 and 146.

One advantage with the multifocal intraocular lens according to thepresent invention is the improved visual quality that can be obtained.

Embodiments of the invention are defined in the dependent claims.

SHORT DESCRIPTION OF THE FIGURES

FIG. 1 shows a calculated Modulation Transfer Function for a bifocalintraocular lens according to the present invention and a conventionalbifocal lens.

FIG. 2. shows a measured Modulation Transfer Function for a bifocalintraocular lens according to the present invention and a conventionalbifocal lens.

FIG. 3. shows the longitudinal chromatic aberration as a function ofwavelength for the near and far focus.

FIGS. 4A and 4B. show the Modulation Transfer Function for a bifocalintraocular lens according to two embodiments of the present inventionand according to a conventional bifocal lens.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention generally relates to a multifocal ophthalmic lensand to methods of obtaining said multifocal intraocular lens that iscapable of reducing the aberrations of the eye for at least one focus.By aberrations in this context is meant wavefront aberrations. This isbased on the understanding that a converging wavefront must be perfectlyspherical to form a point image, i.e. if a perfect image shall be formedon the retina of the eye, the wavefront having passed the opticalsurfaces of the eye, such as the cornea and a natural or artificiallens, must be perfectly spherical. An aberrated image will be fanned ifthe wavefront deviates from being spherical. In this context the termnonspherical surface will refer to rotationally symmetric, asymmetricand/or irregular surfaces, i.e. all surfaces differing from a sphere.The wavefront aberrations can be expressed in mathematical terms inaccordance with different approximate models as is explained in textbookreferences, such as M. R. Freeman, Optics, Tenth Edition, 1990.

In a first embodiment, the present invention is directed to a method ofdesigning a multifocal ophthalmic lens with one base focus and at leastone additional focus capable of reducing aberrations of the eye for atleast one of the foci after its implantation. The base focus may also bereferred to as far field focus and the at least one additional focus, asnear field focus and raid field focus. The method comprises a first stepof characterizing at least one corneal surface as a mathematical model,a second step wherein the mathematical model is employed for calculatingthe resulting aberrations of the corneal surface. An expression of thecorneal aberrations is thereby obtained, i.e. the wavefront aberrationsof a spherical wavefront having passed such a corneal surface. Dependenton the selected mathematical model different routes to calculate thecorneal aberrations can be taken. The corneal surfaces are preferablycharacterized as mathematical models and the resulting aberrations ofthe corneal surfaces are calculated by employing the mathematical modelsand raytracing techniques. An expression of the corneal wavefrontaberrations is thereby obtained, i.e. the wavefront aberrations of awavefront having passed such a corneal surface. Dependent on theselected mathematical model different routes to calculate the cornealwavefront aberrations can be taken. Preferably, the corneal surfaces arecharacterized as mathematical models in terms of a conoid of rotation orin terms of polynomials or a combination thereof. More preferably, thecorneal surfaces are characterized in terms of linear combinations ofpolynomials.

From the information of steps above an ophthalmic lens is modeled, suchthat a wavefront from an optical system comprising said lens and cornealmodel obtains reduced aberrations. The optical system considered whenmodeling the lens typically includes the cornea and said lens, but inthe specific case it can also include other optical elements includingthe lenses of spectacles, or an artificial correction lens, such as acontact lens, a corneal inlay implant or an implantable correction lensdepending on the individual situation.

Furthermore the base power for far vision, the light distributionbetween the at least two foci, and the optical power(s) for theadditional focus/foci, of the ophthalmic lens has to be selected, whichis done according to conventional methods for the specific need ofoptical correction of the eye, for example the method described in U.S.Pat. No. 5,968,095.

Modeling the multifocal lens involves selection of one or several lensparameters in a system which contributes to determine the lens shape forgiven, pre-selected refractive powers. This typically involves theselection of conventional lens parameters such as the anterior radiusand surface shape, posterior radius and surface shape, the lensthickness and the refractive index of the lens, as well as parametersspecific for multifocal lenses. As mentioned above there are a number ofdifferent ways by which to multifocal lenses may be designed. Hence, themultifocal specific parameters depend on what multifocal design that isused.

The multifocal ophthalmic lens according to the present invention can berealized in the form of a multifocal contact lens, a multifocal cornealinlay for aphakic patients, or the like, but it wilt be described indetail in the form of a multifocal intraocular lens. Furthermore themultifocal specific parameters discussed will be limited to parametersapplicable on bifocal lenses of diffractive type, but it should beunderstood that the multifocal lens modeled according to presentinvention can be of any multifocal type or combinations thereof. Abifocal diffractive lens is a combination of a conventional refractivelens and a diffractive lens, the former focused to infinity and thelatter for near vision. A diffractive lens consists of a series ofradial rings or “zones” of decreasing width. Typically, the lightdistribution of a bifocal diffractive lens is set at around 50:50%, thusboth the near and the far foci are accommodated. The diffractive lensmay be formed on the anterior or posterior surface of the conventionallens, or at an intermediate position. The light distribution of thediffractive bifocal lens is determined by the step height of thediffractive zones. The power add for near field focus is determined bythe diameters of the diffractive zones. Theoretically, this isindependent of the refractive indices of the lens and the surroundingmedium.

In practical terms, the lens modeling can be performed with data basedon a conventional bifocal lens, such as the CeeOn® 811E lens fromPharmacia Corp. Values of the central radii of the lens, its thicknessand refractive index are maintained, while selecting a different shapeof the anterior and/or posterior surface, thus providing one or both ofthese surfaces to have a nonspherical shape.

According to one embodiment of the present invention, the anteriorand/or posterior surface of the bifocal intraocular lens is modeled byselecting a suitable aspheric component. Preferably the lens has atleast one surface described as a nonsphere or other conoid of rotation.Designing nonspherical surfaces of lenses is a well-known technique andcan be performed according to different principles and the descriptionof such surfaces is explained in more detail in our PCT patentapplication WO 01/62188, to which is given reference.

The inventive method can be further developed by comparing wavefrontaberrations of an optical system comprising the lens and the model ofthe average cornea with the wavefront aberrations of the average corneaand evaluating if a sufficient reduction in wavefront aberrations isobtained for at least one of the foci. Suitable variable parameters arefound among the above-mentioned physical parameters of the lens, whichcan be altered so as to find a lens model, which deviates sufficientlyfrom being a spherical lens to compensate for the corneal aberrations.

The characterization of at least one corneal surface as a mathematicalmodel and thereby establishing a corneal model expressing the cornealwavefront aberrations is preferably performed by direct corneal surfacemeasurements according to well-known topographical measurement methodswhich serve to express the surface irregularities of the cornea in aquantifiable model that can be used with the inventive method. Cornealmeasurements for this purpose can be performed by the ORBSCAN®videokeratograph, as available from Orbtech, or by corneal topographymethods, such as EyeSys® from Premier Laser Systems. Preferably, atleast the front corneal surface is measured and more preferably bothfront and rear corneal surfaces are measured and characterized andexpressed together in resulting wavefront aberration terms, such as alinear combination of polynomials which represent the total cornealwavefront aberrations. According to one important aspect of the presentinvention, characterization of corneas is conducted on a selectedpopulation with the purpose of expressing an average of cornealwavefront aberrations and designing a lens from such averagedaberrations. Average corneal wavefront aberration terms of thepopulation can then be calculated, for example as an average linearcombination of polynomials and used in the lens design method. Thisaspect includes selecting different relevant populations, for example inage groups, to generate suitable average corneal surfaces.Advantageously, lenses can thereby be provided which are adapted to anaverage cornea of a population relevant for an individual elected toundergo cataract surgery or refractive correction surgery includingimplantation of an IOL or corneal inlays or phakic IOLs. The patientwill thereby obtain a bifocal lens that gives the eye substantially lessaberrations when compared to a conventional spherical lens.

Preferably, the mentioned corneal measurements also include themeasurement of the corneal refractive power. The power of the cornea andthe axial eye length are typically considered for the selection of thelens power in the inventive design method.

Also preferably, the wavefront aberrations herein are expressed as alinear combination of polynomials and the optical system comprising thecorneal model and modeled intraocular lens provides, for at least one ofthe foci and preferably for each foci, a wavefront having obtained asubstantial reduction in aberrations, as expressed by one or more suchpolynomial terms. In the art of optics, several types of polynomials areavailable to skilled persons for describing aberrations. Suitably, thepolynomials are Seidel or Zernike polynomials. According to the presentinvention Zernike polynomials preferably are employed.

The technique of employing Zernike terms to describe wavefrontaberrations originating from optical surfaces deviating from beingperfectly spherical is a state of the art technique and can be employedfor example with a Hartmann-Shack sensor as outlined in J. Opt. Soc.Am., 1994, Vol. 11(7), pp. 1949-57. It is also well established amongoptical practitioners that the different Zernike terms signify differentaberration phenomena including defocus, astigmatism, coma and sphericalaberration up to higher aberrations. In an embodiment of the presentmethod, the corneal surface measurement results in that a cornealsurface is expressed as a linear combination of the first 15 Zernikepolynomials. By means of a raytracing method, the Zernike descriptioncan be transformed to a resulting wave front (as described in Equation(1)), wherein Z.; is the i-th Zernike term and a_(i) is the weightingcoefficient for this term. Zernike polynomials are a set of completeorthogonal polynomials defined on a unit circle. Below, Table 1 showsthe first 15 Zernike terms and the aberrations each term signifies.

$\begin{matrix}{{z\left( {\rho,\theta} \right)} = {\sum\limits_{i = 1}^{15}{a_{i}Z_{i}}}} & (1)\end{matrix}$

In equation (1), ρ and θ represent the normalized radius and the azimuthangle, respectively.

TABLE 1 i Z_(i) (ρ, θ) 1 1 Piston 2 2ρcos θ Tilt x 3 2ρsinθ Tilt y 4{square root over (3)}(2ρ² − 1) Defocus 5 {square root over (6)}(ρ² sin2θ) Astigmatism 1^(st) order (45°) 6 {square root over (6)}(ρ² cos 2θ)Astigmatism 1^(st) order (0°) 7 {square root over (8)}(3ρ³ − 2ρ)sin θComa y 8 {square root over (8)}(3ρ³ − 2ρ)cos θ Coma x 9 {square rootover (8)}(ρ³ sin 3θ) Trifoil 30° 10 {square root over (8)}(ρ³ cos 3θ)Trifoil 0° 11 {square root over (5)}(6ρ⁴ − 6ρ² + 1) Spherical aberration12 {square root over (10)}(4ρ⁴ − 3ρ²)cos 2θ Astigmatism 2^(nd) order(0°) 13 {square root over (10)}(4ρ⁴ − 3ρ²)sin 2θ Astigmatism 2^(nd)order (45°) 14 {square root over (10)}(ρ⁴ cos 4θ) Tetrafoil 0° 15{square root over (10)}(ρ⁴ cos 4θ) Tetrafoil 22.5°

Conventional optical correction with intraocular lenses will only complywith the fourth term of an optical system comprising the eye with animplanted lens. Glasses, contact lenses and some special intra ocularlenses provided with correction for astigmatism can further comply withterms five and six and substantially reducing Zernike polynomialsreferring to astigmatism.

The inventive method further includes to calculate the wavefrontaberrations resulting from an optical system comprising said modeledbifocal intraocular lens and cornea and expressing it in a linearcombination of polynomials and to determine if the bifocal intraocularlens has provided sufficient reduction in wavefront aberrations for oneor more of the foci. If the reduction in wavefront aberrations is foundto be insufficient, the lens will be re-modeled until one or several ofthe polynomial terms are sufficiently reduced. Remodeling the lens meansthat at least one lens design parameter affecting one or more of thefoci is changed. These include the anterior surface shape and centralradius, the posterior surface shape and central radius, the thickness ofthe lens, its refractive index, and the diameters and the step height ofthe diffractive zones. Typically, such remodeling includes changing theshape of a lens surface so it deviates from being spherical. There areseveral tools available in lens design that are useful to employ withthe design method, such as the optical design software packages OSLO andCode-V. The formats of the Zernike polynomials associated with thisapplication are listed in Table 1.

According to one embodiment, the inventive method comprises expressingat least one corneal surface as a linear combination of Zernikepolynomials and thereby determining the resulting corneal wavefrontZernike coefficients, i.e. the coefficient of each of the individualZernike polynomials that is selected for consideration. The bifocal lensis then modeled so that an optical system comprising of said modelbifocal lens and cornea provides a wavefront having a sufficientreduction of selected Zernike coefficients for at least one of the foci.The method can optionally be refined with the further steps ofcalculating the Zernike coefficients of the Zernike polynomialsrepresenting a wavefront resulting from an optical system comprising themodeled intraocular bifocal lens and cornea and determining if the lenshas provided a sufficient reduction of the wavefront Zernikecoefficients for at least one foci of the optical system of cornea andlens; and optionally re-modeling said bifocal lens until a sufficientreduction in said coefficients is obtained for the at least one foci.Preferably, in this aspect the method considers Zernike polynomials upto the 4^(th) order and aims to sufficiently reduce Zernike coefficientsreferring to spherical aberration and/or astigmatism terms. It isparticularly preferable to sufficiently reduce the 11^(th) Zernikecoefficient of a wavefront from an optical system comprising cornea andsaid modeled multifocal intraocular lens, so as to obtain an eyesufficiently free from spherical aberration for at least one of thefoci. Alternatively, the design method can also include reducing higherorder aberrations and thereby aiming to reduce Zernike coefficients ofhigher order aberration terms than the 4^(th) order.

To achieve the desired reduction of aberrations, the bifocal intraocularlens is optimized with respect to unabberrated optical behavior of theoptical system of the eye. In this respect, the optical behavior may beoptimized for either one of the foci or both simultaneously. If the lensis optimized for the base focus, then the lens will give best opticalresult for far vision. Consequently when the lens is optimized for thenear focus, the best performance is achieved in the near vision. Bestover all performance is achieved when the lens is simultaneouslyoptimized for both foci. The diffractive pattern of the bifocal lens maybe formed independently of the lens surface that is modeled to reduceaberrations of the optical system, but it could also be formed on thesame lens surface.

When designing lenses based on corneal characterizations from a selectedpopulation, preferably the corneal surfaces of each individual areexpressed in Zernike polynomials describing the surface topography andthere from the Zernike coefficients of the wavefront aberration aredetermined. From these results average Zernike wavefront aberrationcoefficients are calculated and employed in the design method, aiming ata sufficient reduction of selected such coefficients. In an alternativemethod according to the invention, average values of the Zernikepolynomials describing the surface topography are instead calculated andemployed in the design method. It is to be understood that the resultinglenses arriving from a design method based on average values from alarge population have the purpose of substantially improving visualquality for all users. A lens having a total elimination of a wavefrontaberration term based on an average value may consequently be lessdesirable and leave certain individuals with an inferior vision thanwith a conventional lens. For this reason, it can be suitable to reducethe selected Zernike coefficients only to certain degree or to apredetermined fraction of the average value.

According to another approach of the inventive design method, cornealcharacteristics of a selected population and the resulting linearcombination of polynomials, e.g. Zernike polynomials, expressing eachindividual corneal aberrations can be compared in terms of coefficientvalues. From this result, a suitable value of the coefficients isselected and employed in the inventive design method for a suitablelens. In a selected population having aberrations of the same sign sucha coefficient value can typically be the lowest value within theselected population and the lens designed from this value would therebyprovide improved visual quality for all individuals in the groupcompared to a conventional lens.

One embodiment of the method comprises selecting a representative groupof patients and collecting corneal topographic data for each subject inthe group. The method comprises further transferring said data to termsrepresenting the corneal surface shape of each subject for a presetaperture size representing the pupil diameter. Thereafter a mean valueof at least one corneal surface shape term of said group is calculated,so as to obtain at least one mean corneal surface shape term.Alternatively or complementary a mean value of at least one to thecornea corresponding corneal wavefront aberration term can becalculated. The corneal wavefront aberration terms are obtained bytransforming corresponding corneal surface shape terms using a raytraceprocedure. From said at least one mean corneal surface shape term orfrom said at least one mean corneal wavefront aberration term an bifocalintraocular lens capable of reducing, for at least one of its foci, saidat least one mean wavefront aberration term of the optical systemcomprising cornea and lens is designed.

In one preferred embodiment of the present invention the method furthercomprises designing an average corneal model for the group of peoplefrom the calculated at least one mean corneal surface shape term or fromthe at least one mean corneal wavefront aberration term. It alsocomprises checking that the designed ophthalmic lens compensatescorrectly for the at least one mean aberration term. This is done bymeasuring these specific aberration terms of a wavefront having traveledthrough the model average cornea and the lens. The lens is redesigned ifsaid at least one aberration term has not been sufficiently reduced inthe measured wavefront for at least one of the foci.

Preferably one or more surface descriptive (asphericity describing)constants are calculated for the bifocal lens to be designed from themean corneal surface shape term or from the mean corneal wavefrontaberration terms for a predetermined radius. The spherical radius isdetermined by the refractive power of the lens.

The corneal surfaces are preferably characterized as mathematical modelsand the resulting aberrations of the corneal surfaces are calculated byemploying the mathematical models and raytracing techniques. Anexpression of the corneal wavefront aberrations is thereby obtained,i.e. the wavefront aberrations of a wavefront having passed such acorneal surface. Dependent on the selected mathematical model differentroutes to calculate the corneal wavefront aberrations can be taken.Preferably, the corneal surfaces are characterized as mathematicalmodels in terms of a conoid of rotation or in terms of polynomials or acombination thereof. More preferably, the corneal surfaces arecharacterized in terms of linear combinations of polynomials.

In one embodiment of the invention, the at least one nonsphericalsurface of the bifocal lens is designed such that the lens for at leastone focus, in the context of the eye, provides to a passing wavefront atleast one wavefront aberration term having substantially the same valuebut with opposite sign to a mean value of the same aberration termobtained from corneal measurements of a selected group of people, towhich said patient is categorized. Hereby a wavefront arriving from thecornea of the patient's eye obtains a reduction in said at least oneaberration term provided by the cornea after passing said bifocal lens.The used expression ‘in the context of the eye’ can mean both in thereal eye and in a model of an eye.

In a specific embodiment of the invention, the wavefront obtains reducedaberration terms expressed in rotationally symmetric Zernike terms up tothe fourth order. For this purpose, the surface of the bifocalintraocular lens is designed to reduce a positive spherical aberrationterm of a passing wavefront for at least one of the foci. In this textpositive spherical aberration is defined such that a spherical surfacewith positive power produces positive spherical aberration. Preferablythe bifocal lens is adapted to compensate for spherical aberration forat least one of the foci, and more preferably it is adapted tocompensate for at least one term of a Zernike polynomial representingthe aberration of a wavefront, preferably at least the 11^(th) Zerniketerm, see Table 1.

The selected groups of people could for example be a group of peoplebelonging to a specific age interval, a group of people who will undergoa cataract surgical operation or a group of people who have undergonecorneal surgery including but not limited to LASIK (laser in situkeratomileunsis), RK (radialo keratoectomy) or PRK (photorefractivekeratoectomy). The group could also be a group of people who have aspecific ocular disease or people who have a specific ocular opticaldefect.

The lens is also suitably provided with optical powers. This is doneaccording to conventional methods for the specific need of opticalcorrection of the eye. Preferably the refractive power for the basefocus of the lens is less than or equal to 34 diopters and theadditional focus between 2 and 6 diopters. An optical system consideredwhen modeling the lens to compensate for aberrations typically includesthe average cornea and said lens, but in the specific case it can alsoinclude other optical elements including the lenses of spectacles, or anartificial correction lens, such as a contact lens, a corneal inlay oran implantable correction lens depending on the individual situation.

In an especially preferred embodiment the bifocal intraocular lens isdesigned for people who will undergo a cataract surgery. In this case itis has been shown that the average cornea from such a population isrepresented by a prolate surface following the formula:

$z = {\frac{\left( {1/R} \right)r^{2}}{1 + \sqrt{1 - \left( \frac{1}{R} \right)^{2} + {\left( {{cc} + 1} \right)r^{2}}}} + {adr}^{4} + {aer}^{6}}$

wherein,

the conical constant cc has a value ranging between −1 and 0

R is the central lens radius and

ad and ae are polynomial coefficients additional to the conicalconstant.

In these studies the conic constant of the prolate surface rangesbetween about −0.05 for an aperture size (papillary diameter) of 4 mm toabout −0.18 for an aperture size of 7 mm. According to these results thebifocal intraocular lens to be designed should have a prolate surfacefollowing the same formula. Accordingly a bifocal intraocular lenssuitable to improve visual quality by reducing at least sphericalaberration for at least one focus for a cataract patient based on anaverage corneal value will have a prolate surface following the formulaabove. Since the cornea generally produces a positive sphericalaberration to a wavefront in the eye, a bifocal intraocular lens forimplantation into the eye will have negative spherical aberration termswhile following the mentioned prolate curve. As will be discussed inmore detail in the exemplifying part of the specification, it has beenfound that an intraocular lens that can correct for 100% of a meanspherical aberration has a conical constant (cc) with a value of lessthan 0 (representing a modified conoid surface). For example, a 6 mmdiameter aperture will provide a 20 diopter lens with conical constantvalue of about 1.02.

In this embodiment, the bifocal intraocular lens is designed to balancethe spherical aberration of a cornea that has a Zernike polynomialcoefficient representing spherical aberration of the wavefrontaberration with a value in the interval from 0.0000698 mm to 0.000871 mmfor a 3 mm aperture radius, 0.0000161 mm to 0.00020 mm for a 2 mmaperture radius, 0.0000465 mm to 0.000419 mm for a 2.5 mm apertureradius and 0.0000868 mm to 0.00163 mm for a 3.5 mm aperture radius usingpolynomials expressed in table 1. These values were calculated for amodel cornea having two surfaces with a refractive index of the corneaof 1.3375. It is possible to use optically equivalent model formats ofthe cornea without departing from the scope of the invention. Forexample one or more multiple surface corneas or corneas with differentrefractive indices could be used. The lower values in the intervals arehere equal to the measured average value for that specific apertureradius minus one standard deviation. The higher values are equal to themeasured average value for each specific aperture radius plus threestandard deviations. The reason for selecting only minus one SD(=Standard Deviation) while selecting plus three SD is that in thisembodiment it is convenient to only compensate for positive cornealspherical aberration and more than minus one SD added to the averagevalue would give a negative corneal spherical aberration.

According to one embodiment of the invention the method furthercomprises the steps of measuring the at least one wavefront aberrationterm of one specific patient's cornea and determining if the selectedgroup corresponding to this patient is representative for this specificpatient. If this is the case the selected lens is implanted and if thisis not the case a lens from another group is implanted or an individuallens for this patient is designed using this patient's cornealdescription as a design cornea. These method steps are preferred sincethen patients with extreme aberration values of their cornea can begiven special treatments.

According to another embodiment, the present invention is directed tothe selection of a bifocal intraocular lens of refractive powers,suitable for the desired optical correction that the patient needs, froma plurality of lenses having the same powers but different aberrations.The selection method is similarly conducted to what has been describedwith the design method and involves the characterizing of at least onecorneal surface with a mathematical model by means of which theaberrations of the corneal surface is calculated. The optical system ofthe selected lens and the corneal model is then evaluated so as toconsider if sufficient a reduction in aberrations is accomplished for atleast one foci by calculating the aberrations of a wavefront arrivingfrom such a system. If an insufficient correction is found a new lens isselected, having the same powers, but different aberrations. Themathematical models employed herein are similar to those described aboveand the same characterization methods of the corneal surfaces can beemployed.

Preferably, the aberrations determined in the selection are expressed aslinear combinations of Zernike polynomials and the Zernike coefficientsof the resulting optical system comprising the model cornea and theselected lens are calculated. From the coefficient values of the system,it can be determined if the bifocal intraocular lens has sufficientlybalanced the corneal aberration terms for at least one foci, asdescribed by the Zernike coefficients of the optical system. If nosufficient reduction of the desired individual coefficients is found,these steps can be iteratively repeated by selecting a new lens of thesame powers but with different aberrations, until a lens capable ofsufficiently reducing the aberrations of the optical system for at leastone foci is found. Preferably at least 15 Zernike polynomials up to the4^(th) order are determined. If it is regarded as sufficient to correctfor spherical aberration, only the spherical aberration terms of theZernike polynomials for the optical system of cornea and bifocalintraocular lens are corrected. It is to be understood that the bifocalintraocular lens shall be selected so a selection of these terms becomesufficiently small for the optical system comprising lens and cornea forat least one of the foci. In accordance with the present invention, the11^(th) Zernike coefficient, a₁₁, can be substantially eliminated orbrought sufficiently close to zero for at least one of the foci. This isa prerequisite to obtain a bifocal intraocular lens that sufficientlyreduces the spherical aberration of the eye for at least one of thefoci. The inventive method can be employed to correct for other types ofaberrations than spherical aberration by considering other Zernikecoefficients in an identical manner, for example those signifyingastigmatism, coma and higher order aberrations. Also higher orderaberrations can be corrected dependent on the number of Zernikepolynomials elected to be a part of the modeling, in which case a lenscan be selected capable of correcting for higher order aberrations thanthe 4^(th) order.

According to one important aspect, the selection method involvesselecting lenses from a kit of lenses having lenses with a range ofpowers and a plurality of lenses within each power combinations for farand near foci having different aberrations. In one example the lenseswithin each power combination have anterior surfaces with differentaspherical components. If a first lens does not exhibit sufficientreduction in aberration for at least one of the foci, as expressed insuitable Zernike coefficients, then a new lens of the same powercombination, but with a different surface (aspheric component) isselected. The selection method can if necessary be iteratively repeateduntil the best lens is found or the studied aberration terms are reducedbelow a significant borderline value for at least one of the foci. Inpractice, the Zernike terms obtained from the corneal examination willbe directly obtained by the ophthalmic surgeon and by means of analgorithm they will be compared to known Zernike terms of the lenses inthe kit. From this comparison the most suitable lens in the kit can befound and implanted. Alternatively, the method can be conducted beforecataract surgery and data from the corneal estimation is sent to a lensmanufacturer for production of an individually tailored lens.

The present invention further pertains to a bifocal intraocular lenshaving at least one nonspherical surface capable of transferring, for atleast one foci, a wavefront having passed through the cornea of the eyeinto a substantially spherical wavefront with its center at the retinaof the eye. Preferably, the wavefront is substantially spherical withrespect to aberration terms expressed in rotationally symmetric Zerniketerms up to the fourth order.

In accordance with an especially preferred embodiment, the inventionrelates to a bifocal intraocular lens, which has at least one surface,when expressed as a linear combination of Zernike polynomial terms usingthe normalized format, that has a negative 11th term of the fourth orderwith a Zernike coefficient a₁₁ that that can balance a positivecorresponding term of the cornea, to obtain sufficient reduction of thespherical aberration for at least one foci of the eye afterimplantation. In one aspect of this embodiment, the Zernike coefficienta₁₁ of the bifocal lens is determined so as to compensate for an averagevalue resulting from a sufficient number of estimations of the Zernikecoefficient a₁₁ in several corneas. In another aspect, the Zernikecoefficient a₁₁ is determined to compensate for the individual cornealcoefficient of one patient. The bifocal lens can accordingly be tailoredfor an individual with high precision.

The invention further relates to another method of providing a patientwith a bifocal intraocular lens, which at least partly compensates forthe aberrations of the eye for at least one of the foci. This methodcomprises removing the natural lens from the eye. Surgically removing ofthe impaired lens can be performed by using a conventionalphacoemulsification method. The method further comprises measuring theaberrations of the aphakic eye, not comprising the a lens, by using awavefront sensor. Suitable methods for wavefront measurements are foundin J. Opt. Soc. Am., 1994, Vol. 11(7), pp. 1949-57 by Liang et. al.Furthermore, the method comprises selecting from a kit of lenses a lensthat at least partly compensates for the measured aberrations for atleast one of the foci and implanting said lens into the eye. The kit oflenses comprises lenses of different powers and different aberrationsand finding the most suitable lens can be performed in a manner asearlier discussed. Alternatively, an individually designed lens for thepatient can be designed based on the wavefront analysis of the aphakiceye for subsequent implantation. This method is advantageous, since notopographical measurements of the cornea are need to be done and thewhole cornea, including the front and back surfaces, is automaticallyconsidered.

According to a special embodiment of the present invention the asphericmultifocal lenses designed to reduce aberrations of wavefronts in thefoci arriving from a system of the lens and cornea, as described in theforegoing parts, can provided with means to distribute light among thefoci with purpose of providing the wearer of the lens with a betterfunctional vision. For example, it is desirable to provide the far focusof an aspheric bifocal aberration reducing IOL with more light intensitywhen the pupil is its maximum diameter. In practical terms this willprovide an individual with better visual quality of distant objects indarkness, so driving during night is simplified. There are several knowntechniques to modify the light distribution of multifocal lenses byreducing the step height of the diffractive pattern in the directiontowards the periphery of lens. U.S. Pat. No. 4,881,805 suggestsdifferent routes to use different echelette depth to vary the lightintensity among the different foci of a multifocal lens. U.S. Pat. No.5,699,142 discloses a multifocal intraocular lens with a diffractivepattern having an apodization zone that gradually shifts the energybalance from the near focus to the distant focus. The apodization zoneis construed so that the echelettes of the diffractive pattern graduallyhas a reduced depth towards the lens periphery. By making an appropriateadjustment of the step height (echelette depth), a desired deviationfrom 50-50% distribution between the two foci of a bifocal lens can beobtained.

According to another special embodiment, the aspheric multifocal lensesof the present invention as outlined in the previous parts of thespecification can be provided with means to reduce chromatic aberrationin at least one of its foci. Aspheric monofocal lenses with a capacityto correct both chromatic aberration and other aberrations as induced bythe optical parts of the eye and distort vision has been described inthe International patent application published as WO 02/084281 whichhereby is incorporated as a reference. In this context “chromaticaberration” signifies both monochromatic and chromatic aberrationintroduced by the optical surfaces of eye and eventually also the lensitself.

The multifocal intraocular lenses can generally be of a refractive or adiffractive type of the diffractive type has been described elsewhere ingreater detail. For both alternatives of multifocal IOLs, the chromaticaberration preferably is provided by a surface configured as adiffractive part with a diffractive surface pattern and has a refractivepower to be added to the total lens power. In both alternatives,chromatic aberration reducing surface is designed to compensate for anychromatic aberration introduced by the refractive part of lens and formonochromatic aberrations introduced by said diffractive surfacepattern. As is discussed in WO 02/084281, it is possible to design thelens to reduce chromatic aberration determined from individual eyesurface (i.e. corneas), or to reduce an averaged chromatic aberrationvalue collected from relevant group of individuals (e.g. a mean valuefrom corneas of patients elected to undergo cataract surgery).

In the design process of an aspheric multifocal IOL that is capable ofcorrecting both for chromatic aberrations and other aberrations, such asspherical aberrations, it may also be needed to compensate for otheraberrations, such as spherical aberrations introduced by the diffractivepattern, while performing optional adjustments of the power contributionof the diffractive pattern.

For the example where the asphericity compensate for aberration terms,such as spherical aberration the features providing the lens withmultiple foci already are set, the design process preferably wouldinclude the steps of:

(i) selecting an eye model, suitably the eye model of Navarro (1985),with an aspheric multifocal ophthalmic lens of a predeterminedrefractive power and a predetermined amount of at least onemonochromatic aberration;

(ii) estimating the power of said eye model at different wavelengths, soas to determine the chromatic aberration of the eye model;

(iii) estimating a correction function of how the power varies with thewavelength to be an ideal compensation for said chromatic aberration ofthe eye model;

(iv) finding a linear function of how power varies with the wavelength,which suitably approximates said correction function;

(v) calculating a provisional zone width of a diffractive profilecorresponding to this linear function and also calculating thediffractive power of this diffractive profile;

(vi) reducing the refractive power of the lens by the amount of powercalculated for the diffractive profile;

(vii) estimating a new correction function of step iii), finding a newlinear function of step iv) and calculating a new provisional zone widthand a new diffractive power for a new diffractive profile correspondingto this new linear function;

(viii) adjusting the refractive power of the lens such that the totalpower equals the predetermined power;

(ix) repeating steps vii) to viii) until a suitable combination of arefractive and a diffractive part of the hybrid ophthalmic lens is foundthat both provide the eye model with a predetermined power and with asuitable reduction in chromatic aberration.

In the design process it is preferable for a diffractive bifocal lens tobalance the chromatic aberration between the near and the distant fociin a mariner that resulting lens in a Navarro eye model obtainspolychromatic modulation transfer functions at 50 cycles/mm from a seteye model which approaches the same value (see also Example 4, below)

For the embodiment with a diffractive aspheric multifocal IOL, thediffractive surface pattern correcting for chromatic aberration will bea second diffractive pattern that consists of a number of rings. For theexample, a lens having a total 20 D power with a 2 D power coming fromthe second diffractive pattern, the first zone has a radial width of 1.5mm. In this case, the second diffractive surface pattern is located onthe anterior side of the lens superimposed on the spherical surface.Preferably, the first diffractive pattern then is located on theposterior side of the lens. Also, for a refractive bifocal lens, thechromatic aberration is (slightly) different for the near and far focus,which means that the performance of the near and far focus can bebalanced, using a merit function, of which the modulation transferfunctions at 50 c/mm is an example.

In another special embodiment, the multifocal lens modelled to reduceaberrations of at least of the foci in a optical system comprising thelens and a model cornea without taking considerations to aberrationsthat the cornea will provide a wavefront with when passing the system.This type of lenses will be suitable for individuals with corneas thatgenerate few aberrations or when there is not access to any cornealaberration data. These lenses will be designed with a nonsphericalsurface with a surface design construed to reduce aberrations in awavefront passing said lens that are generated from the lens itself.Typically, such aberrations involve spherical aberration. A suitableexample of this type of multifocal lens is of the diffractive typehaving a diffractive pattern on the lens surface that is capable ofgenerating multiple foci, and more preferably it is a bifocal lens thatdistributes more light to its distant focus than to its near focus.Optionally, it can be provided with the mentioned means to generate adesired light distribution and with a second diffractive pattern tocompensate for chromatic aberrations of the eye

The lenses according to the present invention can be manufactured withconventional methods. In one embodiment they are made from soft,resilient material, such as silicones or hydrogels. Examples of suchmaterials suitable for foldable intraocular lenses are found in U.S.Pat. No. 5,444,106 or in U.S. Pat. No. 5,236,970. Manufacturing ofnonspherical silicone lenses or other foldable lenses can be performedaccording to U.S. Pat. No. 6,007,747. Alternatively, the lensesaccording to the present invention can be made of a more rigid material,such as poly(methyl)methacrylate. The skilled person can readilyidentify alternative materials and manufacturing methods, which will besuitable to employ to produce the inventive aberration reducing lenses.

As is shown in the following examples, the bifocal intraocular lensaccording to the present invention (BRAIOL) outperforms conventionalBIOLs with respect to Modulation Transfer Function characteristics. Morespecifically it has been found that the BRAIOL has a modulation of atleast 0.2 for both foci at a spatial frequency of 50 cycles permillimetre, when designed such that the light distribution between thetwo foci is 50:50%. The measurements are performed in an averageeyemodel using a 5 mm aperture. Surprisingly it has further been foundthat the sum of the modulation at 50 c/mm for the two or more foci ismore than 0.40, and in some cases even above 0.50, independent of thelight distribution, when measured in the model specified above. The factthat the sum of the modulation at 50 c/mm is independent of lightdistribution is illustrated for the case where the light distributionhas a limiting value of 100:0%, which is equivalent to a monofocal lens.Conventional lenses and lenses correcting spherical aberration weredesigned, manufactured and measured. In this situation, the conventionallens has a modulation at 50 c/mm of 0.21, while the design optimized forspherical aberration shows a modulation of 0.6, equivalent to the sum ofthe designed bifocal lens.

Furthermore, the evaluation experiments have revealed that thewavefronts of the 2 foci of a bifocal lens are independent with respectto some of the Zernike terms, but that some of the Zernike terms arecoupled or equal for both. The far majority of this difference is in the‘defocus’ term, which represents the 4 diopters difference between thefocal points. In the design process it has been found that the sphericalaberration part of the wavefront is not very different for the 2wavefronts. This is also true for all other aberrations, apart fromdefocus, tilt and the piston term. Consequently the present inventionmakes it possible to provide a lens with reduced aberrations inessentially the same scale for all foci.

EXAMPLES

General:

A bifocal intraocular lens which corrects the corneal sphericalaberration (BRAIOL) can be modeled based on a conventional bifocal lens(BIOL), in this case the bifocal model 811E, Pharmacia Corp., which is adiffractive lens design made of Poly(MethylMethAcrylate) material. Thepower add of this lens is +4 diopter for reading, which corresponds toreading spectacles of 3 diopters. In this example, the design is adaptedto be used for a silicone material. As a consequence, the step heightsof the diffractive surface profile are increased with the ratio of thereduced refractive indices of the 2 materials.

The lens optic is a combination of a biconvex lens and a diffractivelens. The diffractive surface profile is superimposed onto the sphericalposterior surface of the optic. The diffractive surface profile can bedescribed using conventional sag equations. Examples of equations forthe surface profile are described in the literature. For instance, Cohen(1993, ‘Diffractive bifocal lens design’, Optom Vis Sci 70(6): 461:8)describes the diffractive profile with the equation:

S _(d)(r)=h*{N−r ² /w ²}

-   -   wherein    -   r is the distance from the optical axis    -   h is the maximum profile height (stepheight)    -   N is the zone number    -   w is the width of the first zone

Other equations are also possible. The type of diffractive profile isnot relevant for the working principles. The diffractive profile issuperimposed onto a normal spherical surface, so that the total sagequation becomes

S(r)=S _(s)(r)+S _(d)(r),

where S_(s)(r) is the sag equation of a spherical biconvex lens:

${S_{s}(r)} = \frac{{cv}*r^{2}}{1 + \sqrt{1 - {{cv}^{2}*r^{2}}}}$

-   -   cv=1/R is the curvature of the lens optic    -   R is the radius of curvature of the lens optic

The radius of curvature of the diffractive bifocal lens is equal to theradius of curvature of a monofocal lens having the same power.

Throughout the example the light distribution between the two foci waschosen to be 50%:50%, and the target power add for near vision was +4 D.Other light distributions can be chosen, without changing the principlesof how the methods work. In practice, light distribution between 70%:30%to 30%:70% and near vision add between 3 and 4 diopters have been on themarket. But also outside these ranges the methods should be applicable.

Throughout the example, data from characterization of corneas conductedon a selected population, was used to calculate the resulting cornealaberrations. The anterior corneal surface shapes of a population of 71cataract patients were measured using corneal topography. The surfaceshapes were described using Zernike polynomials. Each surface shape wasconverted into a wavefront aberration. Also the wavefront aberration wasdescribed in Zernike polynomials.

The method is described in example 4 of the patent application WO01/89424 A1.

The terms of the Zernike polynomials are expressed in wavelengths (λ),using the reference wavelength of 550 nanometers (λ=550 nm).

The target in this example is to correct the corneal sphericalaberration by the bifocal IOL. In order to evaluate the designs, atheoretical design cornea was developed, similar to the one described inexample 4 of the patent application WO 01/89424 A1. In the case ofmodelling a monofocal IOL the design cornea can be a 1-surface model,wherein the refractive index of the cornea is the keratometry index of1.3375. For diffractive lenses it is essential to use the real in vivorefractive index surrounding the posterior (diffractive) lens surface.Therefore, a 2-surface model was developed, which has the same on-axisaberrations as the 1-surface model.

The theoretical performance of the prototype design in terms ofsymmetric Zernike coefficients was evaluated for an IOL having a basepower (far vision) of 20 Diopters. An IOL having this power is close towhat is suitable for most cataract patients. However, the design methodand resulting IOL is similar for other lens powers. Typically, IOLpowers range from 4 to 34 diopters, sometimes extend to −10 to +40diopters and can be occasionally produced even outside these ranges.

Example 1

In one embodiment, the lens is biconvex, having radii of curvature of12.15 mm on both the anterior and posterior surface and a centralthickness of 1.1 mm. The anterior surface is aspherized. In an iterativeprocess, the aberration of the optical system of design cornea andbifocal IOL are optimised in order to reduce the wavefront aberration inthe far focus position, in this example the Zernike term Z₁₁,representing the spherical aberration. In this process, the asphericityof the anterior lens surface is used as the design parameter. Theasphericity of the anterior surface is described by a conic constant.The sag equation of the anterior surface is:

${S(r)} = \frac{{cv}*r^{2}}{1 + \sqrt{1 - {{{cv}^{2}\left( {{cc} + 1} \right)}r^{2}}}}$

-   -   wherein cc is the conic constant

Using commercially available optical design software, the variable cccan be optimized to minimize the Zernike term Z₁₁ for the far visionfocal point. The variable cc was determined for an aperture size of 5.1mm. The anterior surface of this BRAIOL has been modified in such a waythat the spherical aberration of the system (cornea+lens) is nowapproximately equal to 0. The resulting value of the conic constant was−29.32. The Z₁₁ coefficient representing spherical aberration for theconventional IOL in the eye model is 3.8λ, while the same coefficientfor the eye model with the designed BRAIOL is 0.01λ, representing areduction of the spherical aberration by a factor of 380. The sameprocess as described above for can similarly be performed for any otherlens power.

Example 2

In another embodiment, the lens is biconvex, having radii of curvatureof 12.15 mm on both the anterior and posterior surface and a centralthickness of 1.1 mm. The diffractive posterior surface is aspherized. Inan iterative process, the aberration of the optical system of designcornea and bifocal IOL are optimised in order to reduce the wavefrontaberration, in this example the Zernike term Z₁₁, representing thespherical aberration, as well as the symmetrical higher order terms Z₂₂and Z₃₇. In this process, the asphericity of the posterior lens surfaceis used as the design parameter. The asphericity of the posteriorsurface is described by a conic constant and 2 higher order terms. Thetotal sag equation is:

${S(r)} = {\frac{{cv}*r^{2}}{1 + \sqrt{1 - {{{cv}^{2}\left( {{cc} + 1} \right)}r^{2}}}} + {{ad}*r^{4}} + {{ae}*r^{6}} + {S_{d}(r)}}$

-   -   wherein:    -   cc is the conic constant    -   ad is the 4^(th) order aspheric coefficient    -   ae is the 6^(th) order aspheric coefficient

Using commercially available optical design software, the variables cc,ad and ae can be optimized to minimize the Zernike terms Z₁₁, Z₂₂ andZ₃₇ simultaneously in the far focal point. The variables are determinedfor an aperture size of 5.1 mm. The posterior surface of this BRAIOL hasbeen modified in such a way that the spherical aberration and the 2higher order terms of the system (cornea+lens) is now approximatelyequal to 0. The optimisation resulted in the posterior surface asphericcoefficients presented in table 2:

TABLE 2 Aspheric coefficient Value Cc −2.53 Ad 9.4e−4 Ae −5.1e−6

The optical results can be expressed as a reduction in the Zernikecoefficients between the conventional BIOL (using cc=ad=ae=0) and thenewly designed BRAIOL, and are presented in table 3:

TABLE 3 Zernike coefficient Conventional BIOL BRAIOL Z₁₁    3.8 λ   0.01λ Z₂₂   0.11 λ −0.003 λ  Z₃₇ −0.07 λ −0.07 λ

Table 3 shows a large reduction of aberration represented by thecoefficients Z₁₁ and Z₂₂ and no significant reduction of coefficientZ₃₇. The same process as described above for can similarly be performedfor any other lens power.

Example 3 Both

In another embodiment, the lens is biconvex, having an anterior radiusof curvature of 12.15 mm, a posterior radius of curvature of 12.59 and acentral thickness of 1.1 mm. The diffractive profile is located on theposterior surface and the anterior surface is aspherized. In aniterative process, the aberration of the optical system of design corneaand bifocal IOL are optimised in order to reduce the wavefrontaberration, in this example the Zernike term Z₁₁, representing thespherical aberration, as well as the symmetrical higher order terms Z₂₂and Z₃₇. In this process, the asphericity of the anterior lens surfaceis used as the design parameter. The asphericity of the anterior surfaceis described by a conic constant and 2 higher order terms. The sagequation of the anterior surface is:

${S(r)} = {\frac{{cv}*r^{2}}{1 + \sqrt{1 - {{{cv}^{2}\left( {{cc} + 1} \right)}r^{2}}}} + {{ad}*r^{4}} + {{ae}*r^{6}}}$

-   -   wherein:    -   cc is the conic constant    -   ad is the 4^(th) order aspheric coefficient    -   ae is the 6^(th) order aspheric coefficient

Using commercially available optical design software, the variables cc,ad and ae can be optimized to minimize the Zernike term Z₁₁, Z₂₂ and Z₃₇simultaneously. Furthermore, in this embodiment the Zernike terms forboth far and near focal points were taken into account in theoptimisation. In this way both far and near focal point were optimisedsimultaneously. As an extra criterion, weight factors were added, tosecure that the lowest order terms were reduced most drastically. Theweight factors were 1, 0.1 and 0.01 for Z₁₁, Z₂₄ and Z₃₇ respectively.The variables are determined for an aperture size of 5.1 mm. Theposterior surface of this BRAIOL has been modified in such a way thatthe spherical aberration and the 2 higher order terms of the system(cornea+lens) is now approximately equal to 0. The optimisation resultedin the posterior surface aspheric coefficients, presented in table 4:

TABLE 4 Aspheric coefficient Value cc −1.02 ad −4.9e−4 ae −4.9e−5

The optical results can be expressed as a reduction in the Zernikecoefficients between the conventional BIOL (using cc=ad=ae=0) and thenewly designed BRAIOL. Since both far and near are taken into account,the vector sum of the far and near Zernike coefficients are displayed intable 5:

TABLE 5 Zernike coefficient Conventional BIOL BRAIOL Z₁₁  5.3 λ 0.08 λZ₂₂ 0.15 λ 0.43 λ Z₃₇ 0.08 λ 0.08 λ

Table 5 shows a large reduction of aberration represented by thecoefficients Z₁₁ and no significant reduction of coefficient Z₂₂ andZ₃₇, indicating that Zernike term Z₁₁ was minimized on the cost of termZ₂₂, while Z₃₇ was as low as reasonably possible already.

The optical quality was further characterized by calculating themodulation transfer function in the eye model, using an aperture of 5 mm(FIG. 1)

These calculation results show that, when compared with a conventionalBIOL, the modulation transfer function of the BRAIOL is increased withat least by a factor 2. Prototype lenses of this design were made andthe modulation transfer function was also measured in an eye model. Thephysical eye model was constructed to have the same wavefrontaberrations as the design model based on the population of 71 cataractpatients. The focal points were determined by focussing at a spatialfrequency of 25, 50, 100 cycles per millimetre. FIG. 2 shows theresults. The results are the averages of 8 BRIOL lenses and 10conventional BIOL lenses, with 3 measurements per lens. The FIG. 2confirms the gain in optical quality that can be achieved with theBRAIOL.

This example clearly shows that the RAIOL design principles can besuccessfully applied on bifocal (or multifocal) lenses. Three approacheswere used: one design with the anterior lens shape optimized for Zernikecoefficient Z₁₁ for far focus combined with a diffractive posteriorsurface. Alternatively a new posterior lens shape was generated byoptimizing the wavefront aberrations of Zernike coefficients Z₁₁, Z₂₂and Z₃₇. Finally, a new anterior lens shape was generated by optimizingfor the Zernike coefficients Z₁₁, Z₂₂ and Z₃₇ and for the far as well asthe near focus. The performance of these 3 types of lenses, in terms ofMTF, showed to be essentially comparable. It was also demonstrated thatthe improvement optical performance as calculated in theory can beconfirmed by measurement of prototype lenses.

The improvement of the BRAIOL, compared to BIOL (model 811E), issignificant. However the improvement is greater for the larger pupils(larger than 3 mm).

The optical form chosen for the new BRAIOL design is an equiconvex lensmade from a silicone with refractive index of 1.458. The sphericalaberration of an average cornea is balanced by the BRAIOL lens yieldinga system without spherical aberration. The front surface of the lens ismodified such that the optical path lengths of all on-axis rays withinthe design aperture are the same producing a point focus. This featurecan be achieved with many lens forms. The BRAIOL lens could therefore bedesigned on a convex-plano, plano-convex, non-equiconvex lens or anyother design yielding a positive lens. The BRAIOL concept could also beextended in order to encompass a negative lens used to correct therefractive errors of the eye. The front surface or back surface couldalso be modified to produce the needed change in optical path differencethat neutralizes the spherical aberration. There are therefore manypossible designs that would achieve the goals of the BRAIOL lens design.

Example 4

Chromatic Correction of Multifocal Aspheric Intraocular Lenses

The correction of chromatic aberration is performed by a diffractivelens. A diffractive multifocal lens already has a diffractive profile inits surface. For a bifocal diffractive lens, this diffractive profileonly has an effect on one of the focal points, usually the near focus.This means that for the near focus, the chromatic aberration is alreadyreduced in some degree, although this was not originally intended.

The chromatic correction by a diffractive lens influences both focalpoints to an (almost) equal amount. Since for bifocal diffractivelenses, the amount of chromatic aberration is not the same in both focalpoints, the amount of chromatic aberration have to be balanced betweenthe two focal points.

Description of the Lens:

The example lens is made of silicone material. Its shape isequi-biconvex. The anterior surface of the lens comprises an asphericrefractive lens, on which a diffractive profile is superimposed. Thediffractive profile has a lens power of 2.0 diopters, while the asphericrefractive lens has a lens power of 18.0 D. The total resulting lenspower is 20 diopters. The width (diameter) of the first zone of thediffractive profile is 1.5 mm, and there are 16 rings needed to fill afull 6.0 mm IOL optic. In the periphery of the lens, the diffractiverings are 94 microns apart from each other.

The posterior surface includes the normal diffractive profile whichgenerates a 4 diopter power add in the near focus.

Eye dimensions, refractive indices and dispersion of the ocular mediaare used as described by Navarro (1985). This eyemodel includes anaspheric cornea. The surface information for the eye model and the lensis given in Table 6. The lens designed is dependent on the eye modelchosen. It must be noted that it is possible to design lenses usingother eye models of actual physiological data from patients.

TABLE 6 APERTURE SRF RADIUS THICKNESS RADIUS MEDIUM NOTE OBJ — 1.00E+201.00E+14 AIR 1 7.72 0.55 2.55 CORNEA ASPHERE 2 6.5 3.05 2.50 AQUEOUS AST— — 2.25 AQUEOUS 4 — 0.9 2.25 AQUEOUS 5 13.511 1 218 SILICONE ASPHERE,DIFFRACTIVE 6 −13.511 18.30 2.08 VITREOUS DIFFRACTIVE IMS −12 0 1 —RETINA CONIC AND POLYNOMIAL ASPHERIC DATA Surface conic constant AD AE 1−0.260000 — — 5 −1.018066 −0.000509 −4.0423e−06 *DIFFRACTIVE SURFACEDATA (symmetric diffractive surface) Kinoform Diffraction constructionKinoform Surface order Design λ order zone depth DFO DF1 5 1 0.550 μm 10.004561 — −0.001

Behavior of the Lens:

38 discrete wavelengths over the visible spectrum of 390 to 760 nm (10nm steps) were used to evaluate the eyemodel including therefractive/diffractive IOL.

The focus point is here defined as the point where the polychromatic MTF(Modulation Transfer Function) has its maximum at 50 cycles/mm. Thepolychromatic MTF is determined by the weighed average of the MTFresults at all wavelengths used. The weighting of the wavelengths wasdetermined by the standard luminance of the eye under photopic lightconditions, which represents the relative sensitivity of the retina fordifferent wavelengths. The actual back focal length (ABFL) values forthe different wavelengths indicate the presence of a chromaticdifference in focus and by definition the amount of longitudinalchromatic aberration. The calculations are performed at a 3.0 mmaperture (pupil). FIG. 3 shows the change in focal point versus thewavelength. The 2 graphs, for far and near vision, are coupled by the 4diopter diffractive power add. Especially for wavelengths higher than550 nm, this example design shows a good balance between the chromaticaberration of the far and the near focal point.

Table 7 and FIGS. 4A and 4B show the modulations at 50 cycles permillimeters for a spherical lens diffractive bifocal lens, a diffractivebifocal lens with an aspherical anterior surface and a diffractivebifocal lens with an aspherical anterior surface with also the chromaticaberration corrected by a 2.0 D monofocal diffractive pattern on theanterior surface. The chromatic correction mainly influences the FARfocal point, since the NEAR focal point is already (in part) correctedby the diffractive bifocal surface.

TABLE 7 monochromatic polychromatic MTF at 50 c/mm MTF at 50 c/mm FARNEAR Limit FAR NEAR Limit Spherical 0.33 0.30 0.83 0.23 0.28 0.83Aspherical 0.34 0.34 0.83 0.23 0.31 0.83 Aspherical, chromatic 0.33 0.340.83 0.29 0.31 0.83 corrected

A number of embodiments have been described above. However, it isobvious that the design could be varied without deviating from theinventive idea of providing a multifocal ophthalmic lens correctingaberration in the eye system.

Therefore the present invention should not be regarded as restricted tothe above disclosed embodiments, but can be varied within the scope ofthe appended claims. For example, the BIOL can be designed to compensatefor non-symmetrical Zernike terms. This would require making surfacesbeing rotationally non-symmetric, which is within the state of the artproduction techniques, demonstrated by cylindrical lenses beingcurrently on the market.

1-159. (canceled)
 160. A multifocal ophthalmic lens having at least one nonspherical surface which when expressed as a liner combination of polynomial terms representing its aberrations is capable of reducing similar such aberration terms obtained in a wavefront having passed the cornea, thereby obtaining an eye sufficiently free from aberrations. 161-163. (canceled)
 164. A lens according to claim 160, wherein said polynomial terms are Zernike polynomials.
 165. A lens according to claim 164, capable of reducing polynomial terms representing spherical aberrations and astigmatism.
 166. A lens according to claim 165, capable of reducing the 11th Zernike polynomial term of the 4th order. 167-174. (canceled) 